Nuclear Reaction Q-Value Calculator

What Is the Q-Value? The Q-value of a nuclear reaction is the energy released (Q > 0) or absorbed (Q < 0) during the reaction. It is calculated from the mass difference between reactants and products, using Einstein’s mass-energy equivalence: E = mc². Q > 0 (exothermic/exoergic): the reaction releases energy. Q < 0 (endothermic/endoergic): energy must be supplied. Every nuclear decay, fusion, and fission reaction has a characteristic Q-value.

The Q-Value Formula Q = (Σm_reactants - Σm_products) × c² Where masses are in atomic mass units (u) and c² = 931.494 MeV/u. One atomic mass unit (u) = 1.66054 × 10⁻²⁷ kg = 931.494 MeV/c². A mass defect of just 0.001 u releases 931 keV, which is a million times what a chemical bond gives up.

Common Nuclear Reaction Types Alpha decay: ᴬZ → ᴬ⁻⁴(Z-2) + ⁴He (alpha particle). Q = M_parent - M_daughter - M_alpha. Beta⁻ decay: n → p + e⁻ + ν̄_e. Q = M_parent - M_daughter (electron masses cancel in atomic masses). Beta⁺ decay: p → n + e⁺ + ν_e. Q = M_parent - M_daughter - 2m_e. Proton capture: ᴬZ + p → ᴬ⁺¹(Z+1) + γ (gamma). Q = M1 + M2 - M_product. Fission: heavy nucleus splits into two medium nuclei + neutrons. Q ~ 200 MeV for U-235. Fusion: D + T → He-4 + n. Q = +17.59 MeV (tokamak fuel reaction).

Every mode above uses atomic masses, not nuclear masses, which is what the tables you will look these up in actually publish. The bookkeeping works out because the electrons balance: in alpha decay the parent carries Z of them and the daughter plus the alpha carry Z between them. Beta⁺ is the one exception, and it is why that mode subtracts two electron masses.

Worked example: radium-226 alpha decay

Ra-226 has an atomic mass of 226.025410 u and decays to Rn-222 at 222.017577 u.

Mass defect = 226.025410 - 222.017577 - 4.002603 = 0.005230 u
Q = 0.005230 × 931.494 = 4.872 MeV

That is the pair the two mass boxes suggest, so type them in and you get exactly this back. Almost all of that 4.872 MeV goes to the alpha particle as kinetic energy; the recoiling radon nucleus takes about 2% of it, since momentum has to balance and the daughter is 55 times heavier.

Famous Q-Values in Physics Deuterium-Tritium fusion: Q = 17.59 MeV, the reaction ITER and every other tokamak is built around. U-235 fission: Q ≈ 202 MeV per fission, the basis of nuclear power and weapons. Solar pp chain: 4p → He-4 + 2e⁺ + 2ν. Total Q ≈ 26.7 MeV per helium nucleus formed. Carbon-14 beta decay: Q = 0.156 MeV, the low-energy beta that makes radiocarbon dating possible.

Energy Units in Nuclear Physics 1 MeV = 10⁶ eV = 1.602 × 10⁻¹³ joules. Nuclear Q-values are typically 0.1 to 200 MeV. Chemical reactions: 1 to 10 eV. Nuclear reactions are 10³ to 10⁸ times more energetic. 1 gram of matter = 9×10¹³ J if fully converted (E = mc²), equivalent to about 21 kilotons of TNT.

Threshold Energy For endothermic reactions (Q < 0), a minimum kinetic energy must be supplied before the reaction can happen at all.

|Q| is the minimum in the center-of-mass frame. In the laboratory frame, where the target sits still and the projectile does the moving, you need more than that, because some of the incoming kinetic energy has to stay locked up as momentum of the whole system:

Threshold energy = |Q| × (1 + m_projectile / m_target)

For a proton fired at a heavy nucleus the correction is under 1%. For a proton on a proton it is a factor of two.